Post on 07-Jul-2018
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
1/72
OPTIMAL SIZING OF A COUNTERFLOW
COOLER FOR FEED PELLETS
By:
STEVEN LITTLETON FOWLER
B.S. Biosystems Engineering
Oklahoma State University
Stillwater, Oklahoma
2004
Submitted to the Faculty of the
Graduate College of theOklahoma State University
in partial fulfillment of
the requirements forthe Degree of
MASTER OF SCIENCE
July, 2008
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
2/72
ii
OPTIMAL SIZING OF A COUNTERFLOW
COOLER FOR FEED PELLETS
Thesis Approved:
Dr. Timothy Bowser
Thesis Adviser
Dr. Danielle Bellmer
Dr. Ray Huhnke
Dr. A. Gordon Emslie
Dean of the Graduate College
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
3/72
iii
Acknowledgments
The author would like to thank the following people: his advisor, Dr. Tim
Bowser, for his help, support, and patience during the duration of the project, the
members of the author’s graduate committee, Drs Raymond Huhnke and Danielle
Bellmer for their input and recommendations as the author progressed through
development of the model included in this research, the personnel currently and formerly
employed at Bliss Industries that assisted the author throughout this research, Dr. John te
Velde and Miss Carla Beckmann for their assistance in translating a research article
originally published in German, and the author’s family and fiancé for their invaluable
support, assistance, and patience.
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
4/72
iv
Table of Contents
Chapter Page
1) Introduction .................................................................................................................... 1
2) Objectives....................................................................................................................... 5
3) Literature Review ........................................................................................................... 6
3.1) Livestock Feed......................................................................................................... 6
3.2) The Pelleting Process .............................................................................................. 7
3.3) Mathematical and Computer Models .................................................................... 12
4) The Computer Model.................................................................................................... 15
5) Debugging the Model ................................................................................................... 32
5.1) Stabilizing the Model ............................................................................................ 32
5.2) Calibrating the Model............................................................................................ 33
5.3) Validating the Model............................................................................................. 43
6) Conclusions .................................................................................................................. 44
7) Recommendations ........................................................................................................ 46
References......................................................................................................................... 47
Appendix A....................................................................................................................... 49
Appendix B ....................................................................................................................... 51
Appendix C ....................................................................................................................... 57
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
5/72
v
List of Tables
Table Page
Table A – 1 ........................................................................................................................49
Table A – 2 ........................................................................................................................49
Table A – 3 ........................................................................................................................50
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
6/72
vi
List of Figures
Figure Page
Figure 1. 1 An illustration of an OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
7/72
vii
Figure 5. 8 Final moisture content for various drying coefficients and differentair flow rates ................................................................................................ 39
Figure 5. 9 Final moisture content for various drying coefficients and different
initial pellet temperatures............................................................................. 39
Figure 5. 10 Final moisture content for various drying coefficients and different
initial pellet moisture contents..................................................................... 40
Figure 5. 11 Estimated cooler profiles using data from Table A – 2, an ambient
temperature of 85 oF (29.4 oC), an initial relative humidity of 49%,
and a total airflow rate of 6000 CFM........................................................... 42
Figure 5. 12 Estimated cooler profiles using data from Table A – 2, an ambient
temperature of 85 oF (29.4 oC), an initial relative humidity of 49%,
and a total airflow rate of 9700 CFM........................................................... 42
Figure B - 1 ...................................................................................................................... 51
Figure B - 2 ...................................................................................................................... 52
Figure B - 3 ...................................................................................................................... 52
Figure B - 4 ...................................................................................................................... 53
Figure B - 5 ...................................................................................................................... 53
Figure B - 6 ...................................................................................................................... 54
Figure B - 7 ...................................................................................................................... 54
Figure B - 8 ...................................................................................................................... 55
Figure B - 9 ...................................................................................................................... 55
Figure B - 10 ..................................................................................................................... 56
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
8/72
viii
List of Symbols
Symbol Description Units
T Air TemperatureoC
Θ Pellet TemperatureoC
W Absolute Air Humidity decimal (kg/kg)
M Average Pellet Moisture Content (d. b.) decimal (kg/kg)
x Cooler Bed Depth inches
t time seconds
h’ Convective Heat Transfer Coefficient W/m2K
a Specific Surface Area 1/m
Ga Air Flow Rate kg/hm2
Gp Pellet Flow Rate kg/hm2
ca Specific Heat of Air kJ/kgK
cp Specific Heat of Pellets kJ/kgK
cw Specific Heat of Water kJ/kgK
cv Specific Heat of Water Vapor kJ/kgK
hfg Latent Heat of Vaporization of Water kJ/kg
Lbed Total Bed Depth inches
dbed Cooler or Bed diameter inches
ni Number of Iterations n/a
ns Number of Finite Differences n/a
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
9/72
ix
Symbol Description UnitsMeq Moisture Equilibrium Content (d. b.) decimal (kg/kg)
D Diffusivity m2 /s
F Linearization Factor s/in
rh Relative Humidity decimal
Pv Vapor Pressure N/m2
Ps Saturation Pressure N/m2
Rv Ideal Gas Constant for Water J/kg K
µ a Air Viscosity kg/m s
ρb Bulk Density kg/m3
ρp Pellet Density kg/m3
dp Pellet Diameter inches
Lp Pellet Length inches
rp Pellet Radius inches
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
10/72
1
1) Introduction
Bliss Industries Inc. currently manufactures and sells a product they call
OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
11/72
2
Figure 1. 1 An illustration of an OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
12/72
3
a system to more effectively determine an appropriate size of an OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
13/72
4
based on ambient conditions of operation, type of product being cooled and conditioned,
and desired production capacity would meet the needs of Bliss Industries.
In this research the author has combined the efforts of other engineers, modern
computer processing capability, simple numerical integration techniques, and easily
accessible software to develop a tool to meet the needs of Bliss Industries. This research
uses models developed to describe the cooling and drying of grains which have been
modified to describe feed pellets. Using these models, the author has developed and
tested a system that can be used to estimate the temperature and moisture profiles for feed
pellets in an OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
14/72
5
2) Objectives
The primary objective of this research is to develop a tool that will help Bliss
Industries determine the appropriate size for an OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
15/72
6
3) Literature Review
3.1) Livestock Feed
The feeding of livestock is a large and diverse industry in the United States and
worldwide. On average, about 250 million tons of materials are fed to livestock animals
each year in the US, and about 600 million tons are fed to livestock worldwide. This
includes material fed to cattle, pigs, chickens, sheep, and goats (USDA, 2005).
Most livestock feed is in the form of grains, roughages, compound feed, and
additives. Whole grains often include corn, oats, wheat, and barley. Roughages are often
celluloid material ranging from hay to cotton seed hulls. Compound feeds are
combinations of various processed grains, roughages, and additives that are processed
and blended together for optimum nutrition. Compound feed is often fed in the form of
meal, crumbles, or pellets. Additives often include protein supplements, trace minerals,
oils, or other concentrated nutrients specific to the species and environment.
Feed pellets, the main focus of this research, encompass a significant portion of
the livestock feed industry. The United States Department of Agriculture (USDA)
conducted a survey of agricultural cooperatives in 2004, and found an estimated 7 billion
dollars of livestock feed was sold in the US in 2004. At least 14% of the feed sold was in
the form of pellets. This translates into at least one billion dollars of pellets sold in the
US. Additionally, these statistics do not account for pellets produced on site at large
livestock producers and not sold (Eversull, 2005).
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
16/72
7
3.2) The Pelleting Process
The purpose of pelletizing grains and roughages for livestock feed is to increase
the efficiency, digestibility, and palatability of these foodstuffs. Pellet shaped feed allows
for easier and more efficient consumption by the animal. Additionally the process
through which the material is steamed, heated, and formed into pellets breaks down the
contents of the pellet for palatability and digestion purposes (Harper, 1998).
Producing pellets from feedstuffs is an integral system combining steps of size
reduction, conditioning, pelleting, and cooling (Thomas, 1997). During the conditioning
step materials are treated with heat, steam, binders, and other additives that allow smaller
particles to combine into larger ones. Once the material is conditioned, it passes into a
pelletizing mill where it is extruded into cylindrical particles. After the pellets have been
extruded they pass into a cooler where the pellets are simultaneously cooled and dried
(Robinson, 1983).
The cooling and drying process is a crucial step in the production of feed pellet
products. Large amounts of energy and cost have been added to pellets prior to the
cooling and drying process (Harper, 1998). Using a dryer that requires a minimal amount
of energy input is desirable to keep the production costs of pellets as low as possible.
Additionally, when pellets are properly cooled and dried, they are less likely to produce
dust, commonly called fines, or spoil from microbial and fungal growth. Fines are
undesirable since they require more effort for the animal to consume and are more likely
to be wasted. Fines also pose both safety and management issues in handling of the
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
17/72
8
pellets. Fines and spoilage are both problems that can be minimized through proper
cooling and drying of pellets.
Various factors affect the cooling and drying process of feed pellets. Very little
research appears in the literature specifically on the cooling and drying of feed pellets.
However, the studies that can be found in the literature conclude that the behavior of feed
pellets can often be closely approximated with expressions developed for grains and
oilseeds: Robinson (1983); Biagi (1986); Maier (1988), and the cooling and drying
process of grains and other food products is essentially a mass and energy balance
(Brooker et al. 1992). Therefore the amount of energy in the air and pellets as well as the
amount of moisture in both the pellets and the air directly affect the cooling and drying
process. Also the method(s) of heat and mass transfer being employed: conduction,
convection, absorption, adsorption, etc. significantly affects the cooling and drying
process in foods and grains (Heldman and Lund, 2007). Thus the type of cooler being
used and the methods of heat and mass transfer the cooler design employs will impact the
cooling and drying process of feed pellets. Finally, if the pellets are cooled too quickly, a
dry crust will form on the surface of the pellet that will hinder moisture migration out of
the pellet and leave the pellet core soft and moist. Once a pellet with this soft moist core
is allowed to reach equilibrium, the pellet will become brittle and produce excess fines
(Hensley, 2006). Thus, factors that affect the performance of a pellet cooler can be
summarized as: cooler type, air flow rate, air temperature, air humidity, pellet flow rate,
pellet temperature, pellet moisture content, and pellet size (Maier, 1988).
There are various types of coolers that can be used to cool and dry pellets once
they leave the mill. Some of the classic designs include: vertical style cooler, horizontal
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
18/72
9
or belt style cooler, mixed rotary style cooler, and counter flow cooler (Maier, 1988). All
of these designs use air as a convection and advection medium, but each design uses
different means of exposing the pellets to the air. The four main methods for exposing
pellets to drying air are the same as the four main drying methods used in grains: cross
flow, concurrent flow, counter flow and mixed flow (Brooker et al. 1992). Figure 2. 1
shows how each method exposes the product to the cooling air.
Figure 2. 1 The four major grain drying methods (Brooker et al. 1992)
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
19/72
10
The various types of cross flow coolers are described in Maier (1988). The cross
flow cooler is often implemented in two styles: vertical and horizontal. Both models have
large airflow requirements In the vertical model, a product moves by gravity through an
air stream which flows perpendicularly through the product stream. The horizontal model
takes up large amounts of floor space, and air is drawn up through a perforated conveyor
belt that carries the product from the inlet to the outlet of the cooler. To minimize the
floor space requirement of horizontal coolers, additional “decks” can be added. Figure
2.2 illustrates the cross flow methods often employed in pellet coolers.
Figure 2. 2 Cross Flow methods of grain and pellet drying and cooling
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
20/72
11
The concurrent cooler method is used in grain drying and requires a heated air
stream to dry the product and a cool air stream to lower the final temperature of the
product. Initially the product is conveyed horizontally and heated with high temperature
air stream that flows in the same direction as the product stream. After the product has
been dried it is then exposed to a stream of cold air to cool the product. This method does
require additional energy to increase the temperature of the air, but it does provide
excellent uniformity in the drying of the product (Brooker et al. 1992).
The mixed rotary style cooler provides some of the advantages of both horizontal
and vertical cross flow coolers. Similar to a horizontal cross flow cooler, control of bed
depth and residence time of the pellets in the cooler can be achieved by adjusting the
speed of the cooler. However the space requirement of the mixed flow cooler is small
similar to the vertical cross flow cooler (Maier, 1988).
The OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
21/72
12
Figure 2. 3 A cross sectional representation of an operating OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
22/72
13
(temperature, concentration, velocity, etc.) with respect to some independent variable
(time, distance, etc.). Numerical integration methods, such as the Euler method, can then
be used to approximate values for the dependent variable with respect to the independent
variable (Davis and Rabinowitz, 1984). Numerical integration computer models can be
used in various facets of agricultural and biological engineering such as the heat and mass
transport that takes place in a feed pellet cooler.
Mathematical models for counter flow coolers exist in the literature. Some models
describe counter flow water cooling towers used in power generation and refrigeration
(Ren, 2006; Kloppers and Kröger, 2005), but these models do not address the issue of
drying biological material. Other models deal with counter flow cooling of biological
material, but do not use air as the cooling medium (Chern, 1989) or do not consider feed
pellets (Bruce and Giner, 1993). However, one model in particular focuses specifically on
the counter flow cooling and drying of feed pellets. This model was developed to
determine the factors that may influence the design of counter flow feed pellet coolers
(Maier, 1988). Maier (1988) developed a counter flow computer model almost twenty
years prior to this project, but the processing capability of most computers has increased
significantly during that time period (Morley and Parker, 2006). The complexity of
Maier’s (1988) model was limited by the large execution time that would be required on
the microcomputers available at that time. However, the work done by Maier (1988)
provides an incredible foundation for the development of a model to describe the counter
flow cooling and drying process of livestock pellets.
Maier (1988) was able to conclude that the bed depth and residence time are “the
most significant design parameters” for a counter flow cooler. Maier (1988) also
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
23/72
14
concluded that initial cooling temperature has a significant impact on the heat and mass
transfer phenomena occurring in the cooler, but the initial relative humidity of the cooling
air is of “minor importance in the design of a counter flow pellet cooler”(Maier, 1988).
The OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
24/72
15
4) The Computer Model
The model developed in this research is designed to operate in Microsoft Excel
2003, simply referred to as Excel. The model used advanced, custom programmed
macros and custom programmed functions written in Visual Basic for Applications or
VBA. The decision to use Excel and VBA was based on several factors: many small
businesses currently use this software for other everyday purposes (Morley and Parker,
2006), Excel and VBA are capable of complex calculations, Excel is capable of
displaying information graphically to allow simple interpretation of the modeling
process, the use of Excel would prevent the need to purchase costly specialized data
analysis software, and the author has considerable experience in custom macro
programming in VBA and Excel.
The model developed in this research uses a set of input variables to estimate the
temperature and moisture profiles of the air and pellets in the OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
25/72
16
Bliss Industries personnel can assign values for the client’s desired production
capacity, pellet dimensions, initial pellet moisture content, and initial pellet
temperature in appropriate fields in the model. Then they will select an OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
26/72
17
The calculations in this research are carried out in SI units with the exceptions of
bed depth which will be measured in inches and the input variables will use American
customary units. These exceptions are for the convenience of Bliss Industries since their
literature and equipment are specified in the American customary system.
Bliss Industries provided the author with data from OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
27/72
18
_
intuitively by the fact that feed pellets are primarily composed of grains and oilseeds.
These equations have been successfully implemented in previous computer models for
the drying and cooling of grains (Bruce and Giner, 1993) and feed pellets (Maier, 1988).
The counter flow equations are:
)('
Θ−+
= T W cGcG
ah
dx
dT
v paa
4. 1
dx
dW G
M cGcG
T chT
M cGcG
ah
dx
d a
w p p p
v fg
w p p p +
Θ−+−Θ−
+=
Θ )()(
' 4. 2
dx
M d
G
G
dx
dW
a
p= 4. 3
=dt
M d A single kernel drying equation 4. 4
Where h’ represents the convective heat transfer coefficient measured in W/m2K, a
represents the specific surface area measured in m-1, T represents the temperature of air
measured in oC, Θ represents the temperature of the pellets measured inoC, Ga represents
the airflow in the cooler measured in kg/hm2, ca represents the specific heat of air
measured in kJ/kgK, Gp represents total pellet flow in the cooler measured in kg/hm2, cv
represents the specific heat of water vapor measured in kJ/kgK, W represents the absolute
humidity of air measured in kg/kg, hfg represents the latent heat of vaporization measured
in kJ/kg, cp represents the specific heat of pellets measured in kJ/kgK, cw represents the
specific heat of water measured in kJ/kgK, M represents the average moisture content of
pellets (dry basis) measured in kg/kg, x represents the bed depth or position in the cooler
measured in inches, and t represents time measured in seconds. Equation 4.4 is often
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
28/72
19
_
presented this way in the literature and defined later since every product will have a
different drying equation (Brooker et al. 1992). Since the OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
29/72
20
( ) [ ]
−−+= ∑
∞
=1
2
2exp
4)0()(
n
n
n
eqeq Dt M M M t M λ λ
4. 9
Where λ n represents the roots of the zero order Bessel function, Meq represents the
equilibrium moisture content (dry basis), and D represents the diffusivity.
Another method requires the use of finite differences on individual pellets for
varying values of pellet radius, r (Maier, 1988). This method uses a theoretical diffusion
equation that can also be found in Brooker et al., (1992):
∂
∂+
∂
∂=
∂
∂
r
M
r r
M D
t
M 12 4. 10
Where M is the local moisture content (dry basis). To solve equation 4.10, it can be
assumed that the surface of the pellet is always at equilibrium with the surroundings and
the moisture content of the pellet core does not change. The solution to equation 4.10 can
then be used to determine the average moisture content at any value of x within the cooler
bed.
Equations 4.9 and 4.10 require an expression for diffusivity, D. Expressions for
diffusivity of feed pellets were proposed by both Maier (1988) and Biagi (1986). Biagi
(1986) determined experimentally that the diffusivity of feed pellets could be
approximated by:
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
30/72
21
Θ
−
×=
−
abs
K
h
m D
547exp10015.1
25 4. 11
Maier (1988) concluded a more appropriate diffusivity approximation could be obtained
by modifying an expression developed for corn by Chu and Hustrulid (1968):
( )
Θ−Θ+−
×=
−
abs
abs
K M
h
mC D
251345.047.5exp10513.1
24 4. 12
Maier (1988) proposed using a value of C = 3 for feed pellets.
Both of these methods for estimating drying rates were determined infeasible for
this research. Results of numerical integration experiments using equation 4.9 yielded
slow drying rates and did not support data provided by Bliss describing the input and
output conditions of OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
31/72
22
Θ−=
abs
R Ak
5023exp 4. 14
The drying constant, k, has units of s-1 and Θabs has units of R. The recommended value
of the drying coefficient, A, for corn is 0.54 (Pabis and Henderson, 1961).
A more commonly used and simpler form of equation 4.13 can be obtained by
assuming that equilibrium moisture content is a constant value (Brooker et al., 1992):
[ ]kt M M M t M eqeq −−+=
exp)0()( 4. 15
Equation 4.15 does not accurately predict the drying of grains due to low initial drying
rates (Brooker et al., 1992). However, in OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
32/72
23
( )F M M R Adx
M d eq
abs
−
Θ−=
5023exp 4. 16
The linearization factor, F, is based on the concept of mass continuity in a steady state
device (Cengel and Boles, 2006). It can be assumed that the position in the cooler and
time are related linearly by a factor, F that has units of s/in and can be defined as:
=
p
B
GF
ρ 15971 4. 17
In order to implement equation 4.17, it was necessary to describe the equilibrium
moisture content of the pellets as a function of bed depth or as a function of other
parameters that are only dependent on bed depth. Information in the literature regarding
the equilibrium moisture content of livestock feed pellets is scarce. The only available
data are sorption isotherms published by Friedrich (1980). Figure 4. 1 shows Friedrich’s
(1980) sorption isotherms and commonly used expressions for Meq of grains and oilseeds
as depicted in Maier (1988).
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
33/72
24
Figure 4. 1 A comparison of sorption isotherms of livestock feed pellets and equilibrium moisture
content equations (Maier, 1988)
In Figure 4. 1 Maier (1988) compared the sorption isotherms of hog, dairy, and
broiler feed pellets published by Friedrich (1980) with various moisture equilibrium
content equations. It can be concluded that the expression for moisture equilibrium
content of soybeans closely approximates the moisture equilibrium content of feed pellets
(Maier, 1988). The equilibrium content of soybeans can be estimated by (Brook and
Foster, 1981):
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
34/72
25
))ln()576.24(98.1ln(066816.0375314.0 rhT M eq +−−= 4. 18
Relative humidity, rh, can be defined as the ratio of the amount of water being
carried by the air and the total amount of water that the air can carry (Ramaswami et al.
2005). It can also be defined as (ASABE, 2005):
s
v
P
Prh = 4. 19
Where Pv , represents the vapor pressure and Ps represents the saturation pressure. The
vapor pressure can be defined as:
v
vatm
v RW
RW PP
+=
287 4. 20
Where the atmospheric pressure, Patm, is in Pa, and Rv is the ideal gas constant for water
vapor and has a value of 416.95 J/kgK. The saturation pressure, P s, can be estimated by
(ASABE, 2005):
−
++++
+= 2
432
exp25.649,105,22 GT FT
ET DT CT BT A
Ps 4. 21
Where A = -27,405.526, B = 97.5413, C = -0.146244, D = 0.12558x10-3
,
E = -0.48502x10-7
, F = 4.34903, and G = 0.39381x10-2
(ASABE, 2005).
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
35/72
26
After obtaining a complete expression for equation 4.4, it was now necessary to
define other parameters in the model equations. Values for the specific heat of air, water,
and water vapor were readily available in a Thermodynamic text. Since the temperature
change of the pellets and air is small in an OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
36/72
27
not available for feed pellets, but it can be assumed that pellets will behave similar to
corn (Maier, 1988). Thus A = 1.2925 and B = 19.961 (Brook and Foster, 1981).
An expression for the convective heat transfer coefficient, h’, in packed beds of
cylinders was determined by Barker (1965). A version of Barker’s (1965) equation
appropriate for grains is (Brooker et al., 1992):
B
a
a p
aa
Gd G AC h
=
µ ' 4. 24
Where the air viscosity, µa, can be calculated as (Brooker et al., 1992):
DT C a += µ 4. 25
For SI units, the coefficients for grains are as follows: A = 0.2755, B = -0.34,
C = 0.06175, and D = 0.000165.
The specific surface area, a, is defined as the amount of surface area per unit
volume of the cooling bed. For cylindrical pellets the specific surface area can be
approximated as (Maier, 1988):
+
−=
p p
p p
p
b
lr
lr a
)(21
ρ
ρ 4. 26
The model developed in this research uses an iterative process to estimate the
temperature and moisture profiles inside the OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
37/72
28
be made for the temperature and moisture profiles. Values for T and Θ are initialized as
the line between Θinitial and Tambient using:
ambient
bed
ambient initial T x L
T xand xT +
−Θ=Θ )()( 4. 27
Values for the average pellet moisture content and absolute humidity profiles are
initialized as constant values of Minitial and Wambient respectively. Finally derivatives for all
moisture and temperature profiles are initialized as a negative 0.1 as an initial estimate
since the temperature and moisture of both pellets and air temperature should decrease as
x increases (Bliss Industries Inc., 1999).
After defining an initial estimate for the temperature and moisture content
profiles, the iterative process can begin. Estimations are calculated for air and pellet
properties such as: relative humidity, specific heat, and latent heat of vaporization that are
dependent on temperature and moisture content. These properties and the initial values
for temperature and moisture can then be used in equations 4.1 – 4.4 to calculate better
estimates for the changes in temperature and moisture for both the air and pellets.
Numerical integration methods can then be used to obtain new estimates of the
temperature and moisture profiles in the cooler. The iterative loop is completed when
new estimates of air and pellet properties are calculated from the new estimates of the
moisture and temperature profiles.
Convergence for this model is evaluated in two ways: the values for the
temperature and moisture content of the product and air do not change between iterations,
or the estimated amount of water entering the air is approximately equal to the estimated
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
38/72
29
amount of water entering the product. The iterative loop is repeated a number of times, n i,
that is greater than or equal to the number of bed slices, ns. Repeating the process until ni
is 250% of ns will allow the model to approach convergence. Numerical integration
experiments using the data in Appendix A indicate an ns value of 200 is appropriate for
most OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
39/72
30
Figure 4. 2 Flow Schematic of the Model Program
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
40/72
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
41/72
32
5) Debugging the Model
5.1) Stabilizing the Model
Once expressions and values had been identified for all parameters in the model
equations, the model was programmed into an Excel and VBA format. A macro was
written to carry out the iterative process discussed previously in Figure 4. 2 and values
from Appendix A were placed into the model for testing.
The initial model exhibited one major flaw: the temperature profiles would
become unstable and exhibit a diverging sinusoidal response before the model could
converge. The pellet temperature, Θ, would show an increase at some point in the cooler,
n j, and then immediately decreased at the next point in the cooler, n j+1. In the next
iteration, the next point, n j+2, would show an increase and point n j+3 would show a
decrease. This divergent phenomenon would proliferate with each iteration until the
entire profile for Θ exhibited a sinusoidal pattern. Also, the magnitude of the difference
between the increases and decreases would escalate as the value of n i increased. A
comparison of equations 4.1 and 4.2 shows that the values of the air and pellet
temperatures are closely linked. So as the pellet temperature values diverged, the air
temperature values behaved similarly.
This divergent phenomenon violates the Second Law of Thermodynamics.
Specifically the Clausius statement, a significant basis of the Second Law of
Thermodynamics, is violated. The Clausius statement infers that heat cannot flow
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
42/72
33
spontaneously from a low temperature body to a higher temperature body without
additional work being done to the system (Cengel and Boles, 2006). Once the pellets
enter the OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
43/72
34
expressions and equations were derived from thermodynamic principles or were used in
computer models describing pellet cooling and drying (Maier, 1988; Biagi, 1986).
The change in moisture content, calculated by equation 4.16, used an empirical
drying coefficient, A. Initially a value for whole corn was used for this coefficient.
However, the drying rate of whole corn is affected by the presence or absence of the tip
cap, pericarp, and hull (Brooker et al., 1992). However, feed pellets are composed of
particles of corn and other grains, roughages, and additives. If the tip cap, pericarp, and
hull of the corn and other grains are present in pellets, they will likely not have the same
effect on drying that is observed in whole kernels. For this research, it was assumed that
feed pellets and whole corn have different values for the drying coefficient, A, in
equation 4.16.
A simple sensitivity analysis was conducted to determine how changing the value
of the drying coefficient would affect the model. Since the OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
44/72
35
for values of the drying coefficient ranging from 0.5 to 2.5. The process was again
repeated using values for ambient temperature of 0oF and 100
oF. Figure 5. 1 illustrates
the results of the data collection.
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F
i n a l M o i s t u r e C o n t e n t
T = 0 F
T = 50 F
T = 100 F
Figure 5. 1 Final moisture content for various drying coefficients and different ambient temperatures
It can be concluded from Figure 5. 1 that ambient temperature has little affect on
the estimate of final moisture content of pellets, and according to the final moisture
content provided in Table A – 1 (7 – 8 %), the drying coefficient has a value between of
1.5 , where the final moisture content was estimated to be 8.2% and 2.2 where the final
moisture content was estimated to be 7.0%.
Other variables were then systematically changed one by one to determine if and
how each variable would affect the final moisture content estimate. The process used to
produce Figure 5. 1 was repeated for all independent variables in the system: ambient
absolute humidity, bed depth, bed diameter, pellet diameter, pellet length, pellet flow
rate, air flow rate, initial pellet temperature, and initial pellet moisture content. Each time
the process was repeated only one independent variable and the drying coefficient were
W = 0.006917Θ = 180 FMin = 12%dbed = 129 inLbed = 60 in
Gp = 50 ton/hGa = 17500 CFMdp = 11/64 inLp = 0.75
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
45/72
36
changed to see how the model performed under various conditions. The results can be
seen in Figures 5. 2 – 10.
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t W =0.00345
W =0.0069
W =0.0138
Figure 5. 2 Final moisture content for various drying coefficients and different ambient humidity
conditions.
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o
n t e n t
Lbed = 30in
Lbed = 60in
Lbed = 90in
Figure 5. 3 Final moisture content for various drying coefficients and different bed depth values
T = 50 F
Θ = 180 FMin = 12%dbed = 129 inLbed = 60 in
T = 50 FW = 0.006917Θ = 180 FMin = 12%dbed = 129 in
Gp = 50 ton/h
Ga = 17500 CFMdp = 11/64 inLp = 0.75
Gp = 50 ton/hGa = 17500 CFMdp = 11/64 inLp = 0.75
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
46/72
37
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
dbed = 120in
dbed = 129in
dbed = 137in
Figure 5. 4 Final moisture content for various drying coefficients and different cooler diameters
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
dp = 1/8in
dp = 11/64in
dp = 1/2in
Figure 5. 5 Final moisture content for various drying coefficients and different pellet diameters
T = 50 FW = 0.006917Θ = 180 FMin = 12%Lbed = 60 in
Gp = 50 ton/hGa = 17500 CFMdp = 11/64 inLp = 0.75
T = 50 FW = 0.006917Θ = 180 FMin = 12%dbed = 129 inLbed = 60 in
Gp = 50 ton/hGa = 17500 CFMLp = 0.75
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
47/72
38
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
Lp = 0.25in
Lp = 0.75in
Lp = 1.5in
Figure 5. 6 Final moisture content for various drying coefficients and different pellet lengths
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
Gp = 50 ton/hr
Gp = 75 ton/hr
Figure 5. 7 Final moisture content for various drying coefficients and different pellet flow rates
It should be noted that Figure 5. 7 does not contain a data series for 25 tons per
hour. The model estimated that the temperature would drop too quickly in this cooler at
such a low product flow rate and the pellets would exit at or close to the initial 12%
moisture content regardless of the value of the drying coefficient.
T = 50 FW = 0.006917Θ = 180 FMin = 12%dbed = 129 in
Lbed = 60 inGp = 50 ton/hGa = 17500 CFMdp = 11/64 in
T = 50 FW = 0.006917Θ = 180 FMin = 12%
dbed = 129 inLbed = 60 inGa = 17500 CFMdp = 11/64 in
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
48/72
39
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
Ga = 8000 CFM
Ga = 17500 CFM
Ga = 35000 CFM
Figure 5. 8 Final moisture content for various drying coefficients and different air flow rates
It should be noted in Figure 5. 8 that an extremely high airflow rate will cool the
bed too quickly and minimize moisture loss.
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n
t e n t
in = 180 F
in = 150 F
Figure 5. 9 Final moisture content for various drying coefficients and different initial pellet
temperatures
Θ
Θ
T = 50 FW = 0.006917Θ = 180 FMin = 12%
dbed = 129 inLbed = 60 inGp = 50 ton/hrdp = 11/64 in
T = 50 FW = 0.006917Min = 12%dbed = 129 in
Lbed = 60 inGp = 50 ton/hrGa = 17500 CFMdp = 11/64 in
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
49/72
40
0.05
0.07
0.09
0.11
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C
o n t e n t
Min = 12%
Min = 10%
Figure 5. 10 Final moisture content for various drying coefficients and different initial pellet
moisture contents
The process was then repeated for a second OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
50/72
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
51/72
42
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70
Bed Depth (in)
T e m p e r a t u r e ( ° C )
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
M o i s t u r e C o n t e n t
T (°C)
Θ (°C)
W (kg/kg)
M (kg/kg)
Figure 5. 11 Estimated cooler profiles using data from Table A – 2, an ambient temperature of 85oF
(29.4oC), an initial relative humidity of 49%, and a total airflow rate of 6000 CFM
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70
Bed Depth (in)
T e m p e r a t u r e ( ° C )
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
M o i s t u r e C o n t e n t
T (°C)
Θ (°C)
W (kg/kg)
M (kg/kg)
Figure 5. 12 Estimated cooler profiles using data from Table A – 2, an ambient temperature of 85
oF
(29.4oC), an initial relative humidity of 49%, and a total airflow rate of 9700 CFM
_
_
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
52/72
43
5.3) Validating the Model
As a validation process, the model was used to estimate the temperature and
moisture profiles for the data in Table A – 3. The model estimated a final moisture
content of 5 – 6% for location 3, lower than the reported 7 – 8% final moisture content.
The information in Table A – 3 was then compared to the other information provided in
Appendix A. A comparison of the information in Table A – 2 and A – 3 reveals that both
coolers are used for similar product streams (15 tons per hour of ¾” pellets), but a larger
cooler was selected for Location 3. Location 3 had a listed relative humidity of 32% and
is more arid than Location 2 with a relative humidity of 49%. After a discussion with
Bliss Industries personnel, a possible reason was identified for the low final moisture
content estimation: the cooler in Location 3 may have been oversized. This can be
supported by the fact that Bliss Industries literature indicates that a model of these
dimensions could process an average of about 35 tons per hour of product (Bliss
Industries Inc., 1999). There are several reasons why an oversized cooler may have been
selected for this location. A few of them include: a client with plans to increase
production in the future, a more appropriately sized cooler may not have been compatible
with the client’s other pelletizing equipment, or an appropriately sized cooler may not
have been immediately available (Edens, 2008). However, it is unclear why this
particular unit was selected for Location 3, but with the use of the model developed in
this research, Bliss Industries may not install oversized OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
53/72
44
6) Conclusions
The goal of this research was to develop a tool that would assist Bliss Industries
personnel in determining the appropriate size of a counter flow style, OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
54/72
45
For this research, only a limited amount of data was available to calibrate and test
the model. Much of the data originally provided by Bliss Industries is for OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
55/72
46
7) Recommendations
The author recommends that future research in this area should include:
1) Additional data on operating OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
56/72
47
References
American Society of Agricultural and Biological Engineers. 2005. Psychrometric Data,
American National Standards Institute Standard and Engineering Practice. St.
Joseph, MI. ASAE D271.2 APR1979 (R2005)
Barker. J.J. 1965. Heat Transfer in Packed Beds. Ind. Chem. Eng. 57: 43 – 51.
Biagi, J.D. 1986. Modeling of the Feed-Pellet Cooling Process. Ph.D. Thesis. Michigan
State University. East Lansing, MI.
Bliss Industries Inc.1999. OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
57/72
48
Edens, S. 2008. Personal Communication. Bliss Industries Inc. Ponca City, OK.
Eversull, E. 2005. Consolidation, Expansion Spark Growth in Cooperative Feed Sales.
USDA Rural Development. Available at:
www.rurdev.usda.gov/rbs/pub/jul05/expansion.htm.
Friedrich, W. 1980. Der Kühlvorgang von Mischfutterpellets und sien Einfluβ auf die
Pelletfestigkeit. Die Mühle und Mischfuttertechnik. 117. 20. 268 - 281
Harper, Allen. 1998. The Importance of Pellet Quality in Hog Feeding. Livestock
Update. Available at:
http://www.ext.vt.edu/news/periodicals/livestock/aps-98_09/aps-969.html
Heldman, D.R. and D.B. Lund. 2007. Handbook of Food Engineering. Second Edition.
CRC Press. Boca Raton, FL.
Hensley P. 2006. Personal Communication. Bliss Industries Inc. Ponca City, OK.
Kloppers, J. C., and Kröger, D. G., 2005, “A Critical Investigation Into the Heat and
Mass Transfer Analysis of Counterflow Wet-Cooling Towers,” Journal of Heat
Mass Transfer, 48: 765–777.
Locke J. 2008. Personal Communication. Bliss Industries Inc. Ponca City, OK.
Maier, D.E. 1988. The Counterflow Cooling of Feed Pellets. M.S. Thesis. Michigan State
University. East Lansing, MI.
Morley, D., C. S. Parker. 2006. Understanding Computers: Today and Tomorrow. Tenth
Edition. Thomson Course Technology. Boston, MA
Pabis, S. and S. M. Henderson. 1961. Grain Drying Theory: II. A Critical Analysis of the
Drying Curve of Shelled Maize. Journal of Agricultural Engineering Research. 6:
272-277
Ramaswami, A., J. B. Milford., and M. J. Small. 2005. Integrated Environmental
Modeling: Pollutant Transport, Fate, and Risk in the Environment. John Wiley &
Sons, Inc. Hoboken, NJ.
Ren, C. 2006. An Analytical Approach to the Heat and Mass Transfer Processes in
Counterflow Cooling Towers. Journal of Heat Transfer. 128:1142-1148.
Robinson, R.A. 1983. Pellet Cooling. Feed Compounding. Milling.12:26-27
United State Department of Agriculture. 2005. National Agricultural Statistic Service.
Agricultural Statistics. Statistics of Grain and Feed. Available at:
http://www.usda.gov/nass/pubs/agr05/05_ch1.PDF
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
58/72
49
Appendix A
Data provided by Bliss Industries describing three OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
59/72
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
60/72
51
_
Appendix B
The following figures represent a sensitivity analysis conducted on the OP>
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
61/72
52
0.04
0.06
0.08
0.1
0.12
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C
o n t e n t
W =0.001842
W = 0.003684
W = 0.007369
Figure B - 2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
Lbed = 30 in
Lbed = 60 in
Lbed = 90 in
Figure B - 3
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
62/72
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
63/72
54
0.04
0.06
0.08
0.1
0.12
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C
o n t e n t
Lp = 1.5 in
Lp = 2.5 in
Lp = 3.5 in
Figure B - 6
0.04
0.06
0.08
0.1
0.12
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
Gp = 7.5 ton/h
Gp = 15 ton/h
Gp = 30 ton/h
Figure B - 7
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
64/72
55
0.04
0.06
0.08
0.1
0.12
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C
o n t e n t
Ga = 3000 CFM
Ga = 6000 CFM
Ga = 12000 CFM
Figure B - 8
0.04
0.06
0.08
0.1
0.12
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C o n t e n t
in = 150 F
in = 180 F
in = 200 F
Figure B - 9
Θ
Θ
Θ
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
65/72
56
0.04
0.06
0.08
0.1
0.12
0.4 0.9 1.4 1.9 2.4
Drying Coefficient
F i n a l M o i s t u r e C
o n t e n t M in = 10%
M in = 12%
M in = 14%
Figure B - 10
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
66/72
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
67/72
58
A = -27405.526B = 97.5413
C = -0.146244
d = 0.000126
E = -0.0000000485
F = 4.34903
G = 0.00394
R = 22105649.25
Rv = 461.915
Ps = R * Exp((A + B * T + C * T ^ 2 + d * T ^ 3 + E * T ^ 4) / (F * T - G * T ^ 2))
Pv = (Patm * W * Rv) / (287 + W * Rv)If Ps = 0 Then Ps = 1E-200
If (Pv / Ps) > 0 Then
If (Pv / Ps) < 1 Then
rh = Pv / Ps
Else: rh = 0.999
End If
Else: rh = 0.001
End If
End Function
'absolute humidity function
'dry bulb temp in K
'rh as decimal
'Patm in Pa
Function W(tempk, rh, Patm)
Dim Ps As Double
Dim Pv As Double
Dim A As Double
Dim B As Double
Dim C As DoubleDim d As Double
Dim E As Double
Dim F As Double
Dim G As Double
Dim R As Double
Dim Rv As Double
Dim T As Variant
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
68/72
59
If tempk > 530 Then tempk = 530
T = tempk
A = -27405.526
B = 97.5413
C = -0.146244
d = 0.000126
E = -0.0000000485
F = 4.34903
G = 0.00394
R = 22105649.25
Rv = 461.915
Ps = R * Exp((A + B * T + C * T ^ 2 + d * T ^ 3 + E * T ^ 4) / (F * T - G * T ^ 2))
W = ((rh / 100) * Ps * 287) / (Patm * Rv - (287 + Rv))
End Function
'convective transfer coefficient
'Ga=kg/h/m^2 d=pellet diameter m Ca=kJ/kgK T = temperature C
Function hprime(Ga, Ca, d, T)
Dim x As Variant
x = 0.2755 * Ca * Ga * (Ga * d / (0.06175 + 0.000165 * T)) ^ -0.34
x = 3.6 * x
'3600s/h and 1kJ/1000J
hprime = x
End Function
'specific surface area m^-1
'ro=pellet radius m l=average pellet length m void= bulk/pellet density
Function sarea(ro, l, void)sarea = (1 - void) * 2 * (ro + l) / (ro * l)
End Function
'latent heat of vaporization kJ/kg
'T in C and M as decimal
Function hfg(T, m)
hfg = (2542.1 - 2.384 * T) * (1 + 1.2925 * Exp(-16.961 * m))
End Function
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
69/72
60
'specific heat of pellets kJ/kgK
Function cp(m)
cp = 1.465 + 3.559 * m
End Function
Function meq(T, rh)
Dim dum As Double
'error prevention
If T < -24.6 Then T = -24.59dum = 0.375 - 0.0668 * Ln(-1.98 * (T + 24.6) * Ln(rh))
'dum = 0.375 - 0.1 * Ln(-1.98 * (T + 24.6) * Ln(rh))
If dum > 1 Then
meq = 1
Else:
If dum < 0 Then
meq = 0
Else: meq = dum
End If
End If
End Function
'basic numerical integrator
'currently uses euler method
Function grate(y1, x1, x2, dy1)
Dim dum As Double
dum = y1 + (x2 - x1) * dy1
grate = dum
End Function
'a more advanced numerical integrator
'uses ymax and ymin to keep numerical integrator reasonable
'uses grate() if dy0 is invalid
Function grateb(y0, y1, x0, x1, x2, dy0, dy1, dy2, ymax, ymin)
Dim dum As Double
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
70/72
61
' the next statement can be removed to use Simpson's method of integration if desired
dy0 = "a"
If IsNumeric(dy0) = False Then
dum = grate(y1, x1, x2, dy1)
Else: dum = y0 + ((x2 - x0) * (dy0 + 4 * dy1 + dy2) / 6)
End If
If dum < ymin Then dum = ymin
If dum > ymax Then dum = ymax
grateb = dumEnd Function
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
71/72
VITA
Steven Littleton Fowler
Candidate for the Degree of
Master of Science
Thesis: OPTIMAL SIZING OF A COUNTERFLOW COOLER FOR FEED PELLETS
Major Field: Biosystems Engineering
Biographical:
Personal Data:
The author was born and raised in Oklahoma. The author is passionate about
agricultural engineering, teaching, and music
Education:B. S. Biosystems Engineering, Oklahoma State University, May 2004
Completed the requirements for the Master of Science in Biosystems
Engineering at Oklahoma State University, Stillwater, Oklahoma in July,
2008.
Experience:
The author has worked in multiple facets of the beef industry including:
breeding, raising, feeding, managing, and meat processing.
The author also has four years of teaching experience in higher education
Professional Memberships:
American Society of Agricultural and Biological Engineers
Tau Beta Pi
Alpha Epsilon
8/18/2019 Optimal Sizing of Counterflow Cooler for Pellets
72/72
Name: Steven Littleton Fowler Date of Degree: July 2008
Institution: Oklahoma State University Location: Stillwater, OK
Title of Study: OPTIMAL SIZING OF A COUNTERFLOW COOLER FOR FEED
PELLETS
Pages in Study: 61 Candidate for the Degree of Master of Science
Major Field: Biosystems Engineering
Scope and Method of Study: The goal of this research is to develop a tool to assist in theselection of an appropriately sized counter flow cooler for feed pellets. Of
primary concern is the OP>